There are a large variety of methods for message transmission over a network. These methods are required to possess a function such as the function of
(A) transmitting a message with sufficient accuracy even though the network suffers from certain faults.
The method has various other functions, depending on the uses and applications. Of these other functions,
(B) the function of not having listening adversaries learn what is being sent; and
(C) the function of verifying whether or not the message received has been tampered with
are among the most important functions.
One of the message transmission methods, having the above mentioned functions (A) to (C), is such a message transmission method in which there are provided a plurality of channels between a transmitting apparatus and a receiving apparatus and which has the following three functions. It is assumed that the number of the channels between the transmitting and receiving apparatuses is n. These functions are:
(1) the function that, even if there is an adversary who is able to tamper with and learn the information data being sent over up to t number of channels, the receiving apparatus is able to receive the message sent by the transmitting apparatus with a predominantly high probability;(2) the function that, even if there is an adversary who is able to tamper with and learn the information data being sent over up to t number of channels, the adversary is entirely unable to estimate the message being sent by the transmitting apparatus; and(3) the function that, even if there is an adversary who is able to tamper with and learn the information data being sent over up to t number of channels, it never occurs that the receiving apparatus receives a value other than the message sent by the transmitting apparatus. It is noted that the above mentioned number t is termed ‘the presumed number of the faulty channels.
It has been known that such message transmission method may or may not be implemented depending on the relationships between the number t and the number n.
For n≧3t+1, the method may be implemented using a system disclosed in Non-Patent Document 1.
If, in case of using the method described in Non-Patent Document 1,n=3t+d+1,d′ is of a value such thatd≧d′≧0.The message is selected from a set of the numbers of elements p^{x}, and the data sent over the respective channels is a set of numbers of elements p^{x−d′}.
Although the foregoing description is for the case of using the channels, there is no limitation to the means for implementing the channels provided that the data may be divided into different sections and that these sections may be sent.    [Non-Patent Document 1] D. Dolev, C. Dwork, O. Waarts, M. Yung: Perfectly Secure Message Transmission. J. ACM 40(1) 17-47 (1993)    [Non-Patent Document 2] G. R. Blakley, C. Meadows: Security of Ramp Scheme. Proc. of Cryptology, Vol. 6, No. 3, pp. 157-167, 1993    [Non-Patent Document 3] D. R. Stinson: On the Connections Between Universal Hashing, Combinatorial Designs and Error-Correcting Codes. Congressus Numerantium 114 (1996), 7-27.